WEAKLY NONLINEAR-THEORY OF FINITE-SIZE EFFECTS IN RESONATORS

General properties of nonlinear wave interactions in systems with periodic boundary conditions (so-called resonators) are studied. The wave field evolution in resonators displays striking, peculiar characteristics because only a small number of waves dominate the energy transfer processes. Indeed, the very fact of setting up boundary conditions is more important than the specific form of the nonlinear evolution equation. Results are presented for a number of wave fields whose evolution is governed by different nonlinear equations: planetary waves, gravity waves, capillary waves, and drift waves in plasmas.